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This paper deals with exact solution for elastic buckling of circular plates resting on internal elastic ring support and elastically restrained against translation at the outer edge. The classical plate theory is used in deriving the governing differential equation for a circular plate resting on internal ring support and linearly restrained at the outer edge and subjected to in-plane compressive load. From the present study it is found that there exists a buckling mode switching from axi-symmetric to asymmetric as we vary the radius of internal elastic ring support. In this case, the buckling mode is not axisymmetric as is generally expected. The plate buckles in an asymmetric mode as the radius of the internal ring support becomes smaller. The cross-over ring support radius varies from 0.1255 to 0.09371 times the plate radius, depending upon the stiffness of the translational spring support at the outer edge. Based on this data, the optimum radius of the internal ring support can be determined. Extensive data is presented in tabular form so that significant conclusions can be arrived at on the influence of translational restraints, Poisson's ratio, and boundary conditions on the buckling behavior of isotropic circular plates. The numerical results obtained from the present study are found to be in close agreement with the previously published data. © School of Engineering, Taylor's University.

Mechanical

School of Mechanical Engineering

Chennai Campus

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Journal of Engineering Science and Technology

Buckling of circular plates with an internal elastic ring support and outer edge restrained against translation

An analytical study is presented for the vibration characteristics of thin circular plates with rotational elastic edge support and resting on an elastic foundation. The Winkler model was used to describe this foundation. The exact analytical method is used to derive the frequency equation of the plate with elastic support and resting on this foundation. Parametric investigations of the vibration of circular plates with an restrained elastically edge against rotation and resting on an elastic foundation have been carried out with respect to various rotational stiffness parameters, foundation stiffness parameters, and boundary conditions. Twelve vibration modes are presented. The location of the stepped region with respect to rotational restraint changed very little and moved from the range of 0:014 26† [10:006 204 8†]-1 134:227 [10:025 94] to 0:017 58 [14:001 133]-6 352:958 2 [14:658 356]. Here, † represents the rotational spring stiffness ratio, and † represents the foundation stiffness ratio. Extensive data are tabulated so that pertinent conclusions can be arrived at on the influence of rotational edge restraint and the foundation parameters of a Winkler foundation on the natural frequencies of uniform thin isotropic circular plates.

The International Journal of Acoustics and Vibration

Free Vibration of Circular Plates with Elastic Edge Support and Resting on an Elastic Foundation

In this paper, transverse vibrations of thin circular plates with guided edge and resting on Winkler foundation have been studied on the basis of Classical Plate Theory. Parametric investigations on the vibration of circular plates resting on elastic foundation have been carried out with respect to various foundation stiffness parameters. Twelve vibration modes are presented. The location of the stepped region with respect to foundation stiffness parameter is presented. © 2012 IAU, Arak Branch. All rights reserved.

Journal of Solid Mechanics

Vibrations of circular plates with guided edge and resting on elastic foundation

This study deals with the exact buckling solutions of annular plates with an elastically restrained guided edge against translation. The classical plate theory is used to derive the governing differential equation for annular plate with elastically restrained guided edge against translation. The buckling mode may not be axisymmetric as previously assumed. In certain cases, an asymmetric mode would yield a lower buckling load. This is due to switching of mode. This work presents the critical buckling load parameters for axisymmetric and asymmetric buckling modes. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational restraints, Poisson's ratio and other boundary conditions on the buckling of uniform isotropic annular plates. The numerical results obtained, are in good agreement with the previously published data. In this paper the characteristic equations are exact, therefore the results can be calculated to any accuracy. Comparison of studies demonstrates the accuracy and stability of this work. Copyright © Taylor & Francis Group, LLC.

Mechanics Based Design of Structures and Machines

Fundamental buckling of annular plates with elastically restrained guided edges against translation

This paper is concerned with the elastic buckling of circular plates with internal elastic ring support and elastically restrained edge against rotation and translation. The classical plate theory is used to derive the governing differential equation for circular plate with internal elastic ring support and elastically restrained edges. This work presents the existence of buckling mode switching with respect to the radius of internal elastic ring support. The buckling mode may not be axisymmetric as previously assumed. In general, the plate may buckle in an axisymmetric mode but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. The optimum radius of the internal elastic ring support for maximum buckling load is also determined. The percentage of increase in buckling load capacity by introducing concentric elastic ring support is determined for the first time. Extensive data are tabulated so that pertinent conclusions can be arrived at on the influence of rotational and translational restraints, Poisson's ratio, and other boundary conditions on the buckling of uniform isotropic circular plates. The numerical results obtained are in good agreement with the previously published data. Copyright © Taylor & Francis Group, LLC.

Buckling analysis of circular plates with elastically restrained edges and resting on internal elastic ring support

Circular plates are commonly used as Structural elements in many Aeronautical, Civil, Mechanical and Naval applications. Even though the circular symmetry of the problem allows for its significant simplification, additional difficulties often arise due to uncertainty of boundary conditions. This uncertainty occurs because, in many practical applications, the edge of the plate is not free, simply supported or clamped. When the plate's boundary conditions depart from the classical cases, elastic translational constraint should be considered. This paper is concerned with the elastic buckling of circular plates with an internal ring support and elastically restrained guided edge against translation. The classical plate theory is used to derive the governing differential equation for circular plate with internal ring support and guided elastic edge support system. This work presents the existence of buckling mode switching with respect to the radius of internal ring support. The buckling mode may not be axisymmetric as previously assumed. The plate may buckle in an axisymmetric mode in general, but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational restraint, Poisson's ratio, and other boundary conditions on the buckling of uniform isotropic circular plates. The numerical results obtained are in good agreement with the previously published data. © Krishtel eMaging Solutions Private Limited.

Advances in Vibration Engineering

Buckling of circular plates with a ring support and elastically restrained edge

This article is concerned with the elastic buckling of circular plates with a support and elastically restrained guided edge against translation. The classical plate theory is used to derive the governing differential equation for circular plate with internal elastic ring support and elastically restrained guided edge support system. This work presents the existence of buckling mode switching with respect to the radius of internal elastic ring support. The buckling mode may not be axisymmetric as previously assumed. In general, the plate may buckle in an axisymmetric mode, but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. The optimum radius of the internal elastic ring support is also determined. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational restraint, Poisson's ratio and other boundary conditions on the buckling of uniform isotropic circular plates. The numerical results obtained are in good agreement with the previously published data.